Elliptic curve isogeny class with Cremona label 126672z (LMFDB label 126672.bd)

• Label: 126672z
• Number of curves: $2$
• Conductor: $126672$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 126672z have rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(3\)	\(1 + T\)
\(7\)	\(1 - T\)
\(13\)	\(1 - T\)
\(29\)	\(1 - T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(5\)	\( 1 - T + 5 T^{2}\)	1.5.ab
\(11\)	\( 1 - T + 11 T^{2}\)	1.11.ab
\(17\)	\( 1 + 4 T + 17 T^{2}\)	1.17.e
\(19\)	\( 1 + 7 T + 19 T^{2}\)	1.19.h
\(23\)	\( 1 + 6 T + 23 T^{2}\)	1.23.g
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 126672z do not have complex multiplication.

Modular form 126672.2.a.z

Isogeny matrix

The \(i,j\) entry is the smallest degree of a cyclic isogeny between the \(i\)-th and \(j\)-th curve in the isogeny class, in the Cremona numbering.

\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with Cremona labels.

Elliptic curves in class 126672z

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
126672.bd2	126672z1	\([0, -1, 0, 1478528, 94892032]\)	\(87267418871946300287/51461562131546112\)	\(-210786558490812874752\)	\([2]\)	\(4147200\)	\(2.5891\)	\(\Gamma_0(N)\)-optimal
126672.bd1	126672z2	\([0, -1, 0, -5976192, 768798720]\)	\(5762851946879949436033/3272968937100635136\)	\(13406080766364201517056\)	\([2]\)	\(8294400\)	\(2.9357\)